{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# 从 0 开始的线性回归" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:33.469430Z", "start_time": "2019-07-03T21:57:31.594438Z" }, "attributes": { "classes": [], "id": "", "n": "1" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import d2l\n", "from mxnet import autograd, np, npx\n", "import random\n", "npx.set_np()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "使用如下创建标号\n", "$$\\mathbf{y}= \\mathbf{X} \\mathbf{w} + b + \\mathbf\\epsilon$$\n", "这里 $\\mathbf{w} = [2, -3.4]^\\top$ 和 $b = 4.2$。" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:33.483583Z", "start_time": "2019-07-03T21:57:33.472382Z" }, "attributes": { "classes": [], "id": "", "n": "2" } }, "outputs": [], "source": [ "def synthetic_data(w, b, num_examples):\n", " X = np.random.normal(0, 1, (num_examples, len(w)))\n", " y = np.dot(X, w) + b\n", " y += np.random.normal(0, 0.01, y.shape)\n", " return X, y\n", "\n", "true_w = np.array([2, -3.4])\n", "true_b = 4.2\n", "features, labels = synthetic_data(true_w, true_b, 1000)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "查看创建的数据。" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:33.993865Z", "start_time": "2019-07-03T21:57:33.486016Z" }, "attributes": { "classes": [], "id": "", "n": "3" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "features: [2.2122064 0.7740038] \n", "label: 6.000587\n" ] }, { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n" ], "text/plain": [ "

" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print('features:', features[0],'\\nlabel:', labels[0])\n", "d2l.set_figsize((3.5, 2.5))\n", "d2l.plt.scatter(features[:, 1].asnumpy(), labels.asnumpy(), 1);" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "读取一个小批量，也就是 `batch_size` 个随机采样到的样本。" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:34.003662Z", "start_time": "2019-07-03T21:57:33.996680Z" }, "attributes": { "classes": [], "id": "", "n": "5" } }, "outputs": [], "source": [ "def data_iter(batch_size, features, labels):\n", " num_examples = len(features)\n", " indices = list(range(num_examples))\n", " random.shuffle(indices) # read at random\n", " for i in range(0, num_examples, batch_size):\n", " j = min(i + batch_size, num_examples)\n", " batch_indices = np.array(indices[i:j])\n", " yield features[batch_indices], labels[batch_indices]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "查看一个小批量。" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:34.075882Z", "start_time": "2019-07-03T21:57:34.005992Z" }, "attributes": { "classes": [], "id": "", "n": "6" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "X =\n", "[[-1.2064103 -0.5134857 ]\n", " [-0.10867531 -1.1554946 ]\n", " [-0.8474277 0.91881126]\n", " [ 0.8370042 -1.1026353 ]\n", " [ 1.5543168 -1.0218834 ]\n", " [ 0.343837 0.02602482]\n", " [-1.2712238 -1.9902322 ]\n", " [ 0.3717077 0.9300072 ]\n", " [-0.6205473 0.7588377 ]\n", " [-0.8431705 -0.42457297]]\n", "y =\n", "[ 3.5305307 7.916799 -0.62370265 9.621203 10.769879 4.792636\n", " 8.41412 1.7626055 0.3863677 3.9524884 ]\n" ] } ], "source": [ "batch_size = 10\n", "for X, y in data_iter(batch_size, features, labels):\n", " print('X =\\n%s\\ny =\\n%s' % (X, y))\n", " break" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "随机初始化模型权重并附上梯度。" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:34.082441Z", "start_time": "2019-07-03T21:57:34.077502Z" }, "attributes": { "classes": [], "id": "", "n": "7" } }, "outputs": [], "source": [ "w = np.random.normal(0, 0.01, (2, 1))\n", "b = np.zeros(1)\n", "\n", "w.attach_grad()\n", "b.attach_grad()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "定义模型和损失函数。" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:34.090815Z", "start_time": "2019-07-03T21:57:34.086013Z" }, "attributes": { "classes": [], "id": "", "n": "9" } }, "outputs": [], "source": [ "def linreg(X, w, b):\n", " return np.dot(X, w) + b\n", "\n", "def squared_loss(y_hat, y):\n", " return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "定义优化算法。" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:34.097896Z", "start_time": "2019-07-03T21:57:34.093948Z" }, "attributes": { "classes": [], "id": "", "n": "11" } }, "outputs": [], "source": [ "def sgd(params, lr, batch_size):\n", " for param in params:\n", " param[:] = param - lr * param.grad / batch_size" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "训练。" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2019-07-03T21:57:42.097735Z", "start_time": "2019-07-03T21:57:34.100263Z" }, "attributes": { "classes": [], "id": "", "n": "12" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "epoch 1, loss 0.040532\n", "epoch 2, loss 0.000148\n", "epoch 3, loss 0.000050\n", "Error in estimating w [ 0.00038743 -0.0003047 ]\n", "Error in estimating b [0.00041628]\n" ] } ], "source": [ "lr, num_epochs = 0.03, 3 # 学习率和数据迭代周期。\n", "net, loss = linreg, squared_loss\n", "\n", "for epoch in range(num_epochs):\n", " for X, y in data_iter(batch_size, features, labels):\n", " with autograd.record():\n", " l = loss(net(X, w, b), y)\n", " l.backward()\n", " sgd([w, b], lr, batch_size)\n", " train_l = loss(net(features, w, b), labels)\n", " print('epoch %d, loss %f' % (epoch + 1, train_l.mean()))\n", " \n", "print('Error in estimating w', true_w - w.reshape(true_w.shape))\n", "print('Error in estimating b', true_b - b) " ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.1" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }